If you could think of travelling further then think about Spain. Cambrils Park is open from Easter onwards and is absolutely fantastic for children (see their website for piccies). If you're caravanning then it is a bit of a treck for small children, but if you're wanting a mobile home then you can fly to Reus (lots of low cost flights) then it's only about 6 kilometres to the site from the airport. Once on site you'll have almost all the facilities you need, and the remainder (beach, town, etc.) are all within walking distance.
It has two pools, one with attractions for the children, but an area for adults, lovely lawned areas around, and a supermarket, pizzeria, restaurant, bar, take-away, bread shop, and small coffee bar - and they are all open from the beginning of season.